GAZA CITY, Gaza Strip — Israeli troops Saturday uncovered more than a dozen cross-border tunnels and battled Gaza militants on the second day of an open-ended ground operation as the Palestinian death toll climbed past 330. The Israeli military said it had severely diminished the arsenal of Hamas, the Islamic militant group ruling Gaza, but the militants have continued to fire rockets. In the northern Gaza Strip, Palestinian officials reported intensified Israeli airstrikes, shelling and numerous civilian casualties. Gaza Health Ministry spokesman Ashraf al-Kidra said the new round of strikes raised the death toll from the 12-day offensive to more than 330 Palestinians, many of them civilians and nearly a fourth of them under the age of 18. In Israel, a Gaza rocket killed a man near the southern city of Dimona and wounded four people, police spokesman Micky Rosenfeld said, marking the second Israeli civilian casualty from the fighting. An Israeli soldier was killed after the start of the ground operation. The Israeli military said during its first 24 hours on the ground in Gaza troops discovered 13 tunnels into Israel — some as deep as 30 yards — that could be used to carry out attacks. Israel says it launched the offensive to deal with that threat. On Saturday, the military said it thwarted a second infiltration attempt through just such a tunnel, killing one militant and forcing the others to return to Gaza. The military also said it has hit 2,350 targets in Gaza, including 1,100 rocket launchers, during the 12 days of fighting. Militants have fired more than 1,600 rockets since July 8.